`z_1 = 1 + i, z_2 = 2 - 3i`, verify the following. ` bar(z_1 . z_2) = bar z_1 . bar z_2`

For z=2+3i, verify the following: bar bar z = z

For z=2+3i, verify the following: (z- bar z ) = 6i

For z=2+3i, verify the following: z bar z = abs(z)^2

For z=2+3i, verify the following: (z+ bar z ) is real

For any two complex numbers, z_1 and z_2 , prove that Re( z_1 z_2 ) = [(Re( z_1 ). Re( z_2 )] - [Im( z_1 ). Im( z_2 )]

If z^2 = -24-18i , then z=

If arg(z) = theta , then arg(bar z) =

If z_1 = a+ib and z_2 = c+id are complex numbers such that abs(z_1) = abs(z_2) = 1 and Re(z_1barz_2) = 0 , then the pair of complex numbers w_1 = a+ic and w_2 = b+id satisfies

If z = 3 + 5i, then represent z, bar z , -z, - bar z in Argand's Diagram.